Week 7, clip 7

Timepoint:  15:33.8

1) On the previous graph, the velocity of stars at a radius of R=17 kpc (kiloparsecs) was still v=220 km/s. What would this measurement imply for the mass of the Milky Way?

Answers:
1) The accepted range is [1e11,3e11]

Explanation:
M / M_sun = (P / 1 year)^-2 * (R / 1 AU)^3

P_star = P_sun * v_sun * R_star / ( v_star * R_sun )

The velocity remains the same, so the period of the star's motion is

P_star = 230 Myr * ( 17 kpc / 8 kpc ) = 488.75 Myr

Inputting these values for period and radius into the original formula, we get

M / M_sun = (4.8875e8)^-2 * (1.7e4 * 206265)^3

M / M_sun = 1.8e11

This is 180 billion solar masses and about twice the value suggested by the Sun's orbit.